The electrical untwisting of a homeotropically aligned smectic \(C^*\) liquid crystal
This paper employs the continuum theory of Leslie et al. to examine the effect of a uniform electric field applied parallel to the layers of a sample of ferroelectric smectic \(C^*\) liquid crystal. The sample is homeotropically aligned between two large, horizontal flat plates and strongly anchored at the boundaries. Seeking solutions that depend only upon the spatial Cartesian coordinate \(z\), which denotes distance across the plates, the authors show that the resulting Euler-Lagrange equations yield two distinct types of solution for the \(c\)-director. One represents the more natural helical or twisted \(C^*\) phase given by \(c = (\cos \varphi (z), \sin \varphi (z), 0)\), while the other denotes a constant \(C\)-type phase where \(\varphi (z) = m \pi\) for some integer \(m\). To distinguish between various possibilities the authors make an energy comparison, anticipating that the configuration associated with the least energy is the one that will be observed in practice. It is found that arrangements with 0, 1 or 2 twists can be energetically favourable depending upon the applied field strength, while those with more than 2 twists are never energetically favourable. In particular, they determine a critical field strength \(E_c\) above which it is energetically favourable for the helical structure to unwind. In this event the \(c\)- director becomes aligned perpendicular to the applied field and parallel to the associated spontaneous polarization vector. The authors proceed to examine the effect of sample thickness on \(E_c\) and derive an expression for \(E_c\) in a large sample. Finally, they discuss the effect of director reorientation when the direction of the applied field is reversed.
scientific article; zbMATH DE number 798890